This invention relates to a position measuring method and a semiconductor exposure apparatus using the same. More particularly, the invention is concerned with a position measuring method and a semiconductor exposure apparatus using the same, which is particularly suitably applicable, for example, in a semiconductor exposure apparatus for projecting and printing an electronic circuit pattern onto a semiconductor substrate, to perform position measurement for an alignment mark of a wafer, to be used for precise alignment, or to perform relative alignment between a wafer and a mask, between a mask and a certain reference position in an apparatus, and between components in an apparatus, for example.
Precise position measurement for an article is used in various fields, such as work machines or robots, for example, and further improvements in its precision have been desired. As regards recent semiconductor devices, the degree of integration of each device is increasing more and more, as can be represented by DRAM, and the linewidth of a pattern to be formed on the semiconductor device is decreasing more and more. In these situations, in a process for measuring the relative position of a reticle and a wafer and for aligning them with each other, which process is an essential technique in a semiconductor exposure apparatus, a further improvement of precision is a critical matter.
A conventional semiconductor exposure apparatus as well as examples of conventional wafer alignment methods will be described below.
FIG. 2 is a schematic view of a semiconductor exposure apparatus. Denoted in the drawing at R is a reticle (original), and denoted at W is a wafer (substrate). Denoted at 1 is a projection optical system. Denoted at 2 is an alignment illumination means, and denoted at 3 is a beam splitter. Denoted at 4 and 5 are imaging optical systems. Denoted at 6 is an image pickup device, and denoted at 7 is an A/D (analog-to-digital) converter. Denoted at 8 is an integration device. Denoted at 10 is a stage driving means, and denoted at 11 is an X-Y stage which is movable two-dimensionally.
While in FIG. 2 only one alignment optical system G for X-direction measurement is illustrated, there is an additional alignment optical system (not shown) for performing Y-direction measurement, like the X-direction measurement. In the semiconductor exposure apparatus shown in FIG. 2, the relative position of the reticle R and the wafer W is detected, and then they are brought into alignment with each other. Thereafter, exposure light is projected from an exposure illumination light source (not shown), by which an electronic circuit pattern formed on the reticle R is projected and transferred to the wafer W, placed on the X-Y stage 11, through the projection optical system 1.
The mask-to-wafer alignment in the apparatus of FIG. 2 will be described below.
The alignment illumination device 2 emits non-exposure light (to which a resist is not sensitive). The light emitted from the illumination device 2 goes through the beam splitter 3, the reticle R and the projection optical system 1, and it illuminates an alignment mark formed on the wafer W. FIGS. 3A and 3B are schematic views for explaining the alignment mark, and it comprises plural rectangular patterns of the same shape. The light reflected by the alignment mark goes again through the projection optical system 1 and the reticle R, and it is reflected by the beam splitter 3. Then, after passing through the imaging optical system 5, it produces an image WM of the alignment mark upon the image pickup surface of the image pickup device 6. The image pickup device 6 then functions to photoelectrically convert the thus formed image WM of the mark, and a signal converted is applied to the A/D converter 7 where it is transformed into a two-dimensional digital signal array. The integration device 8 serves to set a processing window WP (FIG. 3B) to the wafer mark image as digitalized by the A/D converter 7. Further, the integration device 8 operates to perform integration processing in the window WP along the Y direction, to transform the two-dimensional imagewise signal into a one-dimensional mark waveform S(x) such as shown in FIG. 3A. The position measuring device 9 in FIG. 2 serve to measure the position of the alignment mark, on the basis of the one-dimensional waveform S(x) as outputted from the integration device 8.
The procedure described above is repeated, by which positional information is produced in relation to plural measurement points. On the basis of this positional information as well as information related to the relative position of the reticle R and the image pickup device 6, having been detected beforehand, the stage driving means 10 moves the X-Y stage 11 to accomplish alignment between the mask and the wafer.
Next, the method of measuring the alignment mark position in the position measuring device 9 will be explained.
FIG. 4 illustrates an example of a conventional alignment mark position measuring method. In regard to FIG. 4, for simplicity of explanation, a case where an alignment mark is provided by a single rectangular pattern will be described. If an alignment mark is provided by plural rectangular patterns, similar operations may be repeated.
In FIG. 4, a registration calculation step S102 is a process for calculating the centricity (degree of registration) of the mark, and repeated calculations are made with respect to a certain mark position measurement range having been preset. For example, as shown in FIG. 5, by repeating the registration calculation step S102 to a mark waveform S(x)1, the registration degree r(x)1 can be determined.
Now, two examples for conventional registration degree calculating processes will be explained.
In a first example, the degree of registration between a mark waveform (detected waveform) and a preset template waveform (reference waveform) is calculated while shifting the template position. The template position where the registration degree becomes highest is taken as the mask position. Hereinafter, this method will be called a xe2x80x9ctemplate matching methodxe2x80x9d. The registration degree can be calculated, on the basis of the difference between the mark waveform and the template waveform. The registration degree r(x) at a position x upon the mark waveform can be determined in accordance with equation (1) or equation (2), below.                               r          ⁡                      (            x            )                          =                  1                                    ∑                              k                =                                                      -                    w                                    /                  2                                                            w                /                2                                      ⁢                          |                                                S                  ⁡                                      (                                          x                      +                      k                                        )                                                  -                                  T                  ⁡                                      (                    k                    )                                                              |                                                          (        1        )                                          r          ⁡                      (            x            )                          =                  1                                    ∑                              k                =                                                      -                    w                                    /                  2                                                            w                /                2                                      ⁢                                          {                                                      S                    ⁡                                          (                                              x                        +                        k                                            )                                                        -                                      T                    ⁡                                          (                      k                      )                                                                      }                            2                                                          (        2        )            
in equation (1) and (2), S(x) is the mark waveform, T(x) is the template waveform, and w is the waveform width for calculating the registration degree, and it corresponds to the width of the template.
A second example is that a mark waveform is laterally and symmetrically folded at a certain position and the registration degree between the left-hand side and right-hand side mark waveforms is calculated while shifting the folding position. The folding position with which the registration degree becomes highest is taken as the mark central position. Hereinafter, this method will be called a xe2x80x9cfolding methodxe2x80x9d. The registration degree can be calculated on the basis of a difference between the left-hand and right-hand mark waveforms. The registration degree r(x) at a position x upon the mark waveform can be determined in accordance with equation (3) or equation (4) below.                               r          ⁡                      (            x            )                          =                  1                                    ∑                              k                =                0                                            w                /                2                                      ⁢                          |                                                S                  ⁡                                      (                                          x                      +                      k                                        )                                                  -                                  S                  ⁡                                      (                                          x                      -                      k                                        )                                                              |                                                          (        3        )                                          r          ⁡                      (            x            )                          =                  1                                    ∑                              k                =                0                                            w                /                2                                      ⁢                                          {                                                      S                    ⁡                                          (                                              x                        +                        k                                            )                                                        -                                      S                    ⁡                                          (                                              x                        -                        k                                            )                                                                      }                            2                                                          (        4        )            
A highest registration calculation step S103 in FIG. 4 is a process for determining the highest registration degree position (template position or folding position) as can be calculated by the registration calculation at step S102, such that the thus determined position is taken as the mark center position. The position where the registration degree becomes highest can be determined, at a precision less than the resolving power of a sensor, in accordance with a gravity center calculation to the registration degree at each position x or with a quadratic function approximation, for example. For example, equation (5) below is a method wherein the mark center position MC is determined through gravity center calculation.                               M          c                =                                            ∑                              k                =                ss                            se                        ⁢                          kr              ⁡                              (                k                )                                                                        ∑                              k                =                ss                            se                        ⁢                          r              ⁡                              (                k                )                                                                        (        5        )            
In the equation above, a range from xe2x80x9cssxe2x80x9d to xe2x80x9csexe2x80x9d is the range of registration degree being preset for gravity center calculation.
The description made above concerns the alignment mark position measuring method to be performed with the position measuring means 9. While the foregoing description relates to wafer position measurement, the position measuring method described above is applicable also to mask (reticle) position measurement or any other position measurement for a component or a unit in a semiconductor exposure apparatus such as a stage, for example. Further, it can be applied to relative alignment between a reticle (mask) and a certain reference position in the apparatus, or between any other components of the apparatus.
In alignment marks to be used in a semiconductor exposure apparatus, however, there is non-uniformness in surface level difference of each alignment mark or non-uniformness in film thickness of a photoresist covering the mark. Such non-uniformness causes deformation in shape of a mark waveform to be inputted into an image pickup device, and it in turn causes a measurement error.
If for example, a mark waveform S(x)2 (FIG. 5), having its shape deformed due to non-uniformness of a resist coating or of the surface level difference of the alignment mark, is inputted, then the registration degree r(x)2 also changes, thus causing an error with respect to calculation of the largest registration degree position. Such a measurement error attributable to deformation of the waveform shape may not be so critical conventionally. Since, however, further improvements in alignment precision are required more and more, it is very desirable to reduce the measurement error due to deformation of a waveform shape.
It is accordingly an object of the present invention to reduce a measurement error due to a change in shape of a mark waveform, caused by any factor such as non-uniformness of a resist coating or of a surface level difference of an alignment mark.
In accordance with an aspect of the present invention, there is provided a position measuring method for measuring a position of a mark formed on an object, said method comprising the steps of: detecting a mark waveform obtainable from the mark; detecting a difference between the detected mark waveform and a reference waveform; correcting at least one of the mark waveform and the reference waveform on the basis of the detected difference; and determining the position of the mark on the basis of the correction.
In one preferred form of this aspect of the present invention, in said correcting step, a parameter for a correction function for determining a correction amount with respect to each position in the waveform is calculated so as to minimize the difference, wherein at least one of the mark waveform and the reference waveform is corrected on the basis of the correction amount as determined by the parameter of the correction function.
In one preferred form of this aspect of the present invention, the reference waveform is based on a template waveform prepared beforehand.
In one preferred form of this aspect of the present invention, the reference waveform is based on one of a left-hand half and a right-hand half of the mark waveform.
In one preferred form of this aspect of the present invention, the parameter of the correction function is calculated in accordance with a least square method.
In one preferred form of this aspect of the present invention, the correction function comprises an equation representing a straight line.
In one preferred form of this aspect of the present invention, in said mark position determining step, a degree of registration between the corrected mark waveform and the reference waveform is calculated, wherein the position of the mark is determined in accordance with a position where the registration degree is highest.
In one preferred form of this aspect of the present invention, the registration degree is calculated on the basis of a correlation coefficient between the corrected mark waveform and the reference waveform.
In accordance with another aspect of the present invention, there is provided a semiconductor exposure apparatus wherein wafer alignment is performed on the basis of detection of a position of an alignment mark formed on a wafer, and wherein a pattern of a reticle is transferred to the wafer, said apparatus comprising: first detecting means for detecting a mark waveform obtainable from the alignment mark; second detecting means for detecting a difference between the detected mark waveform and a reference waveform; correcting means for correcting at least one of the mark waveform and the reference waveform on the basis of the detected difference; and determining means for determining the position of the alignment mark on the basis of the correction.
In one preferred form of this aspect of the present invention, said correcting means is arranged to calculate a parameter for a correction function for determining a correction amount with respect to each position in the waveform so as to minimize the difference, wherein said correcting means corrects at least one of the mark waveform and the reference waveform on the basis of the correction amount as determined by the parameter of the correction function.
In one preferred form of this aspect of the present invention, the reference waveform is based on a template waveform prepared beforehand.
In one preferred form of this aspect of the present invention, the reference waveform is based on one of a left-hand half and a right-hand half of the mark waveform.
In one preferred form of this aspect of the present invention, the parameter of the correction function is calculated in accordance with a least square method.
In one preferred form of this aspect of the present invention, the correction function comprises an equation representing a straight line.
In one preferred form of this aspect of the present invention, said mark position determining means calculates a degree of registration between the corrected mark waveform and the reference waveform, wherein the position of the mark is determined in accordance with a position where the registration degree is highest.
In one preferred form of this aspect of the present invention, the registration degree is calculated on the basis of a correlation coefficient between the corrected mark waveform and the reference waveform.
In accordance with a further aspect of the present invention, there is provided a device manufacturing method which includes an exposure process to be performed by use of a semiconductor exposure apparatus as recited above.
These and other objects, features and advantages of the present invention will become more apparent upon a consideration of the following description of the preferred embodiments of the present invention taken in conjunction with the accompanying drawings.